The optimum execution order of queries in linear storage
Information Processing Letters
Approximation algorithms for NP-hard problems
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
A transformation for a heterogeneous, multiple depot, multiple traveling salesman problem
ACC'09 Proceedings of the 2009 conference on American Control Conference
Analysis of Christofides' heuristic: Some paths are more difficult than cycles
Operations Research Letters
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This paper introduces a new generalized version of the Traveling Salesman Problem (TSP) in which nodes belong to various color classes and each color class must be visited as an entity. We distinguish the cases of the problem for which the colors are either pre-assigned or can be selected from a given subset of colors. We establish computational complexity and provide concise formulations for the problems that lend themselves to derive tight lower bounds. Exact solutions for special cases and a two-phase heuristic for the general case are provided. Worst case performance and asymptotic performance of the heuristic are analyzed and the effectiveness of the proposed heuristic in solving large industrial size problems is empirically demonstrated.